Many problems in business decision making can be modeled as mathematical optimization problems such as mixed-integer programming problems, or satisfiability problems, which are part of artificial intelligence research. Using (commercial) software packages for solving these problems, companies such as AirFrance, Amazon, Microsoft, Uber or HP apply these techniques to diverse areas like assigning flights to aircrafts, facility location, project scheduling, project portfolio optimization, network design, vehicle routing, security testing, formal verification of hardware and many others.

These software packages now allow the solution of problem-instances with up to millions of decision variables in reasonable time. However, the solvability often depends on the structure of the encoded problem, and from a theoretical computer science perspective, both mixed- integer programming problems and satisfiability problems belong to a family of hard problems. Moreover, with the advent of big data, the instances, which are needed to be solved are becoming lager and larger. Thus, to tackle the issues imposed by theoretical hardness and ever-increasing problem-sizes, further improvements in the solution algorithms are needed. In the research carried out within this “seed”-project “OPTIM-AI”, we want to improve solution algorithms for mathematical optimization problems and satisfiability problems, by i) hybridizing the solution algorithms and ii) transferring ideas between the different scientific domains.